denotes the degenerate part of \(X_{n+1}\) . In modern terminology one would
identify \(sX_n\)  with the latching object \(L_nX\)  of \(X\) 
(see (REF )) and say that a simplicial space
\(X\)  in \(s{K}\)  is proper if and only if it is Reedy cofibrant for the
Reedy model structure on \(s{K}\)  associated to the
Strøm model structure on \({K}\)  (see Theorem 4.4.4 of [1]}).
